To calculate the mass of magnesium chlorate (\( \text{Mg(ClO}_3\text{)}_2 \)) in the sample, use the following formula:
\[ \text{mass} = \text{moles} \times \text{molar mass} \]
- Calculate the number of moles in the solution:
The molarity (M) is given, which is defined as: \[ M = \frac{\text{moles}}{\text{liters of solution}} \]
We are given:
- Molarity = 4.02 mol/L
- Volume = 300 mL = 0.300 L
Using the formula to calculate moles: \[ \text{moles} = M \times \text{liters of solution} = 4.02 , \text{mol/L} \times 0.300 , \text{L} = 1.206 , \text{mol} \]
- Calculate the molar mass of \( \text{Mg(ClO}_3\text{)}_2 \):
- Molar mass of Mg = 24.31 g/mol
- Molar mass of Cl = 35.45 g/mol
- Molar mass of O = 16.00 g/mol
Now calculate the molar mass of \( \text{Mg(ClO}_3\text{)}_2 \): \[ \text{Molar mass} = 24.31 , \text{g/mol} + 2 \times (35.45 , \text{g/mol}) + 6 \times (16.00 , \text{g/mol}) \] \[ = 24.31 + 70.90 + 96.00 = 191.21 , \text{g/mol} \]
- Calculate the mass of magnesium chlorate: \[ \text{mass} = \text{moles} \times \text{molar mass} = 1.206 , \text{mol} \times 191.21 , \text{g/mol} \] \[ = 230.57 , \text{g} \]
Conclusion: There seems to be a discrepancy, as the answers provided don't match this calculation. The value calculated indicates that the mass should be approximately 230.57 g, which does not correspond to any of the provided answer options.
Upon re-evaluating, the mass calculated (230.57 g) is correct according to the mole and molarity calculaion applied, but it appears that the options given were likely an error or miscommunication.
If relying solely on provided options, you might look for the most closely related option scientifically, but none align with the calculations.
Hence, if based solely on physically computed results, none of the selection options a, b, c, or d are correct relative to the calculation above yielding 230.57 g as the determined mass.